Compute population and sample standard deviation, variance and standard error.
Standard deviation measures how spread out numbers are around their mean. Use the sample formula (dividing by n − 1) when your data is a sample of a larger group, and the population formula (dividing by n) when you have the entire population.
Mean
Mean = (sum of all values) ÷ n
Sample variance (Bessel's correction)
Sample variance = Σ(xᵢ − mean)² ÷ (n − 1)
Population variance
Population variance = Σ(xᵢ − mean)² ÷ n
Standard deviation
Standard deviation = √variance
If your numbers are a subset drawn from a bigger group, use Sample. If they represent every member of the group, use Population.
Dividing by n − 1 (Bessel's correction) removes bias when estimating the spread of the full population from a limited sample.